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Bounds on the Nuclear World
When defining bounds on the nuclear world, it is important to start by defining terms. Nuclear matter is a special case of hadronic matter, matter made of three quarks and the gluons which act to link them. Nuclear matter is composed of the most inherently stable types of quarks - up and down. There are environments in which other kinds of quarks are needed to make a particle as stable as possible, Astrophysicists write of strange stars, stars whose cores are at such extreme temperature and pressure that strange, charmed, and even bottom quarks might be the most stable way to arrange hadronic matter. There is something called quark-gluon plasma, which may have existed just after the universe began, and which has probably been observed in particle accelerators. Those things aren't nuclear matter. They exist because of their environment. Nuclear matter is different. A piece of nuclear matter may spontaneously fission, eject other pieces of nuclear matter, or give off energy in the form of leptons (electrons and neutrinos) or photons - but it never spontaneously turns into a different kind of hadronic matter. Nuclear matter can be described without describing its environment. Up and down quarks make protons and neutrons. Nuclear matter is composed of up quarks, down quarks, and gluons. Not everything made of protons and neutrons is nuclear matter. There's evidence that neuron stars have a layer of "nuclear pasta" about 800-1000 meters below their surfaces. Pasta is huge, macroscopic chunks of nuclear matter which are stable because pressure is so high that equilibrium between protons, electrons, and neutrons makes free neutrons so abundant that they drift in an out of the pasta without hindrance. Change the environment, and pasta changes with it. Pasta has no more independent existence than a shadow does. To be nuclear matter, something must be definable without referring to its environment. The term "cell of nuclear matter" means a collection of protons and neutrons, all of which are contained within a common nuclear potential well formed by the gluons which are part of the enclosed set of protons and neutrons. The word "contained" does not mean "confined" in this case. It is completely permissible for neutrons or, for that matter smaller cells, to drift out. Atomic nuclei are cells of nuclear matter in which the particles are confined to the potential well. Bring a collection of Z protons and N neutrons together into a cell with A total particles. To a first approximation, that cell looks like a drop of liquid. Nuclear forces bind the particles together, while electrical forces tear it apart. We know about droplets and we know about charge. We can build equations that rest on first principles which describe droplets and charge quantitatively. We can also measure the parameters that make those equations work right when applied to cells of nuclear matter. This is called the "liquid drop model" (LDM); and it yields an equation called the semi empirical mass formula (SEMF), which computes the energy released when Z protons and N neutrons become a cell Z,N or Z,A of nuclear matter. That's called binding energy, and it does not have to be positive. If it is positive, you've got a nucleus. If not, cell Z,A might be impossible. Cell Z,A might also be possible, because there's a gap between being and non-being. If cell Z,A has negative binding energy (Eb), it needs dE = -1*Eb to form. It can pop into existence, provided it disappears within an interval of time, dt, defined by dE*dt = hbar/2. That's called energy-time uncertainty. There's some high-level-physics debate about what that equation means, but little argument that the equation itself is incorrect. As dE gets bigger, though, dt has to get smaller, and that limits the size of what can be a cell of nuclear matter. Among the most generally-applicable rules applying to the universe is this: information cannot travel faster than light. Each particle in Z,A has a fixed size, meaning the cell itself has a fixed volume. It may change shape, but it cannot shrink or grow. Z,A can only pop into being if information can cross it during the time it exists. Otherwise, its various components occupy different realities - they are not causally connected. Z,A can meaningfully exist only if the dE it needs is small enough so that dt is long enough for light to cross the cell. Making dt the length of time for light to cross a proton makes dE = {hbar/2} / dt as big as possible. If Eb >= (-1) * {hbar/2} / dt(proton) for a given Z,A, that cell might be possible. (Remember, less negative is bigger than more negative.) That sets a boundary on the size of cells of nuclear matter. It's a boundary, though, not a limit. The math is straightforward, but it indicates that cells with the most protons, cells with the most neutrons, and cells with the most particles are all different sets of cells. The total number of cells possible, when computed as indicated above, is under 831000. The maximum number of protons appears to be around 670, but is definitely under 680. A cell of nuclear matter is more complicated than a droplet of particles, true, but energies are so big at this point that internal structure doesn't make any difference.